Interpretation of a parameter table of NLME analysis
2026-01-28
NLME parameter table (fixed-effect parameters)1
NLME parameter table example (random-effect parameters)1
Fixed-effect parameters
Parameter descriptions
Parameter abbreviations with unit: CL/F (L/h)
Parameter labels (optional): \(\theta_1\)
Parameter descriptions: Apparent central clearance
Footnotes:
- Full name for abbreviations?
- How were RSE or CI calculated
Fixed-effect parameters: Point estimates
- Output file:
.ext
- Final point estimates in the row with
Iteration=-1000000000.
Point estimates
Back-transform model parameters when necessary
Fixed-effect parameters: Uncertainty (SE)
- Output file:
.cov
- SE of a parameter: \(SE=sqrt{diag}\)
- Although also available in
.ext row Iteration=-10000000001.
\[
\begin{bmatrix}
\mathbf{x_{11}} & x_{12} & x_{13} & \dots & x_{1n} \\
x_{21} & \mathbf{x_{22}} & x_{23} & \dots & x_{2n} \\
\vdots & \vdots & \vdots & \ddots & \vdots \\
x_{d1} & x_{d2} & x_{d3} & \dots & \mathbf{x_{dn}}
\end{bmatrix}
\]
Fixed-effect parameters: Uncertainty (RSE)
Fixed-effect parameters: Uncertainty (confidence interval)
- Compute CI of transformed parameters:
- Parametric (symmetrical):
- Assuming normal distributions: estimates \(\pm\) 1.96*SE.
- Non-parametric (asymmetrical):
- Bootstrap, LLP, SIR and Bayesian (week 6).
Random-effect parameters
- Majority of the elements are similar to the fixed-effect parameters:
- Parameter descriptions, abbreviations, and labels.
- Point estimates (
Iteration=-1000000000 in .ext).
- Uncertainty: SE, RSE or CV.
- Footnotes:
- Full name for abbreviations?
- How were RSE or CI calculated
- Report \(CV\%\) for BSV terms.
- Report \(Corr\) for covariance terms.
- Report \(CV\%\) or \(SD\) for proportional or additive RUV, respectively
- Report shrinkage.
- Footnotes: how were \(CV\%\) and \(SD\)of BSV and RUV calculated.
Random-effect parameters: CV% of BSV
- A log-normal distribution is commonly used for model BSV.
- Avoid negative values in individual PK parameters (e.g., CL).
CL=TVCL* EXP(ETA(1))
- \(CV\% = sqrt{e^{\omega_{1,1}^2}-1} \times 100\%\)
- If a normal distribution is used instead
CL=TVCL+ETA(1)
- \(CV\%=sqrt{\omega_{1,1}^2} \times 100\%\)
- If a logit-normal distribution is used:
F=EXP(THETA(1)+ETA(1))/(EXP(THETA(1)+ETA(1))+1)
- Variability depends on mean.
- \(CV\%\) is not appropriate, \(SD\) is calculated instead using R functions like
logitnorm::momentsLogitnorm1
Random-effect parameters: Corr of covariance terms
- \(Corr=\frac{COV_{p1,p2}}{sqrt{VAR_{p1}} \times sqrt{VAR_{p2}}}\)
- \(COV_{p1,p2}\): estimated covariance between parameters 1 and 2 (p1 and p2).
- \(VAR_{p1}\): estimated variance of p1.
- \(VAR_{p2}\): estimated variance of p2.
- Example: \(Corr_{(CL/F,V2/F)}=\frac{0.0703}{sqrt{0.114} \times sqrt{0.0824}}=0.0725\)
Random-effect parameters: CV% or SD for RUV
Combined error model: Y = IPRED*(1+EPS(1))+EPS(2)
- Report \(CV\%\) for proportional error term: \(CV\%=sqrt{\sigma^2_{1,1}}\)
- Report \(SD\) for additive error term: \(SD=sqrt{\sigma^2_{2,2}}\)
Random-effect parameters: Shrinkage (\(\eta\) shrinkage)
- When the individual data brings only few information about the individual parameter value, the individual estimates (e.g., empirical Bayes estimates, EBEs) is close to (or “shrinks” to) population mean1.
- Output file:
.shk
- \(\eta_i-shrinkage = 1-\frac{SD_{\eta_i}}{\omega}\) (standard)
- \(\eta_i-shrinkage = 1-\frac{VAR_{\eta_i}}{\omega^2}\)
\(\eta\) shrinkage1
- High shrinkage (e.g., SD shrinkage > 30%):
- Doesn’t necessarily mean the model is unacceptable.
- Typically occurs when individual data is sparse (e.g., sparse PK sampling).
- So inadequate information to estimate the EBE of a parameter.
- EBE distribution may not reflect the actual ones.
- Diagnostic plots using EBEs are misleading (hiding or suggesting wrong ones):
- Correlation among \(\eta\)s.
- Covariate-parameter relationship.
- DV vs. IPRED
Random-effect parameters: Uncertainty (confidence interval)
- Compute CI of transformed parameters:
- Parametric (symmetrical):
- Assuming normal distributions: estimates \(\pm\) 1.96*SE.
- Non-parametric (asymmetrical):
- Bootstrap, LLP, SIR and Bayesian (week 6).